Math Problem Statement

Find the value using log and antilog table: 3 .82 ÷[(4.347 x √.06063) ÷ (.8721)²]

Solution

To solve this problem using log and antilog tables, we will follow these steps:

Expression:

3.82(4.3470.06063)(0.8721)2\frac{3.82}{\frac{(4.347 \cdot \sqrt{0.06063})}{(0.8721)^2}}

Step 1: Simplify the denominator

Part 1: 0.06063\sqrt{0.06063}

Using square root tables: 0.060630.246\sqrt{0.06063} \approx 0.246

Part 2: 4.3470.060634.347 \cdot \sqrt{0.06063}

4.3470.2461.0694.347 \cdot 0.246 \approx 1.069

Part 3: (0.8721)2(0.8721)^2

Using log tables:

  • Logarithm of 0.87210.8721: log0.87210.0594\log 0.8721 \approx -0.0594
  • Multiply by 2: 0.05942=0.1188-0.0594 \cdot 2 = -0.1188
  • Antilog of 0.1188-0.1188: antilog(0.1188)0.758\text{antilog}(-0.1188) \approx 0.758

Now divide 1.0691.069 by 0.7580.758: 1.0690.7581.411\frac{1.069}{0.758} \approx 1.411

So the denominator becomes 1.4111.411.


Step 2: Simplify the numerator

The numerator is 3.823.82.

Step 3: Final division

Now divide 3.823.82 by 1.4111.411: 3.821.4112.71\frac{3.82}{1.411} \approx 2.71


Final Answer:

The value of the expression is approximately: 2.71\boxed{2.71}

Would you like me to show detailed steps on how logarithms and antilogs were calculated?


Relative Questions:

  1. How do you calculate square roots using logarithmic tables?
  2. What is the significance of using logarithms in division or multiplication?
  3. How can logarithm tables simplify solving complex expressions?
  4. What is the process for finding antilogs from log tables?
  5. How do errors in table approximations affect final results?

Tip: Always verify intermediate results when using logarithmic tables to avoid compounding errors.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Antilogarithms
Square Root
Division

Formulas

log(ab) = log(a) + log(b)
antilog(x) = 10^x
Square root approximation using logarithms

Theorems

Properties of logarithms
Antilogarithmic calculations

Suitable Grade Level

Grades 10-12